So, you've got a shape on your scene, and you want to move it along a non-linear path. You could create a couple dozen keyframes and work with easing to get it just right, but Motion Paths allow you to animate a shape along any arbitrary path.

To begin with, we need a shape that we want to animate on the path. In the example here, I've got a simple green ellipse. You don't have to name them, but I did to make it easier later on. You can use any element, including a control or a layout container filled with other elements.

You can convert any shape or path into a motion path. A rectangle, ellipse or anything you can think of. Let's start by using the pencil tool to draw a shape.

If you can't find the Pencil tool, right click the Pen tool, until the flyout menu appears and select the pencil from it. I've increased the stroke thickness here so you can see it more easily.

Next, we need to convert that path into a Motion Path. The command is under Object > Path > Convert To Motion Path. The path that we're going to animate along has to be the only thing selected in order for this to work. When you select Convert To Motion Path, a dialog will come up asking which element is to be the target.

Select the Object that will be moving, in my case, the GreenLight. Now, when you press OK, the circle will move so that it's centered on the beginning of the path. Press Play, and you'll see the ellipse move along the line you've drawn.

A couple other things to notice. You're now in Timeline recording mode, and a new timeline was created for you, named Timeline1. If you wanted the animation in a specific timeline, you just needed to have that timeline already selected when you did the Convert To Motion Path command.

The geometry for the path has been moved into the motion path now, so you can delete the line we drew, and the circle will still follow the path.

Now, use the direct selection tool (That's the white arrow), and select the circle. You'll see adorners on the screen indicating the path that the circle will follow.

You can click and drag those adorners to modify the path, and when you hit play, the circle will follow the new path.

Now, if you expand the GreenLight in the timeline, you'll see that there's an animation on the RenderTransform. Expand that and you'll keep going through the animation path until you find the Motion Path itself. It's shown as a grey bar bordered with two blue handles.

By default, the motion path animation takes 2 seconds from beginning to end, but you can change this time by clicking and dragging the handles on the end of the motion path.